All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
11 does not divide any of them (Posted on 2012-12-26) Difficulty: 1 of 5
How many palindromes below 10000 (i.e. between 0 and 9999 inclusively) are not divisible by 11?
List them.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Just counting (spoiler) | Comment 1 of 3
A number is divisible by 11 if and only if the sum of its odd-numbered digits (1st digit, 3rd digit, 5th digit, etc.) minus the sum of its odd-numbered digits are divisible by 11.  Thus, all palindromes with an even number of digits are divisible by 11.  Thus, we must only consider palindromes with an odd number of digits.

All 10 one-digit numbers ( 0, 1, ... 8, 9) qualify.
Also, all 90 of the 3 digit palindromes except:
  121
  242
  363
  484
  616
  737
  858
  979

In other words, 10 + 90 - 8 = 92.  Too many for me to list.

  Posted by Steve Herman on 2012-12-26 17:20:54
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (5)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information